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Theorem fneq1i 5217
Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq1i.1  |-  F  =  G
Assertion
Ref Expression
fneq1i  |-  ( F  Fn  A  <->  G  Fn  A )

Proof of Theorem fneq1i
StepHypRef Expression
1 fneq1i.1 . 2  |-  F  =  G
2 fneq1 5211 . 2  |-  ( F  =  G  ->  ( F  Fn  A  <->  G  Fn  A ) )
31, 2ax-mp 5 1  |-  ( F  Fn  A  <->  G  Fn  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1331    Fn wfn 5118
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-fun 5125  df-fn 5126
This theorem is referenced by:  fnunsn  5230  fnopabg  5246  f1oun  5387  f1oi  5405  f1osn  5407  ovid  5887  tfri1d  6232  frec2uzrand  10185  frec2uzf1od  10186  frecfzennn  10206  dfrelog  12955  nninfsellemeqinf  13265
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